After x3y2 are multiplied inside the bracket, we can eliminate factors which occur in both the numerator and denominator.
x3y2y1−1xy+1=x3y2y1−x3y21xy+x3y21=yx3y2−xyx3y2+x3y2=x3y−x2y+x3y2
where we have used
yx3y2=yx3yy=x3y,
xyx3y2=xyxxxyy=xxy=x2y